Quasi-classical ground-state energies for equally mixed vectorial and scalar attractive power potentials

Summary

Quasi-classical evaluations for the ground-state energies of the Dirac Hamiltonian with equally mixed vectorial and scalar attractive power potentialsV _s(r) = V_v(r) = V_n(r) have been established. Such calculations proceed forn⩽⩽2, whereV _n(r) = C_n/rⁿ andnC _n < 0. The present evaluations reproduce exactly the actual Coulomb results insofar as the underlying phase-space quantum equals unity. It turns out that the onset of the scalar potentials enhance the validity degrees characterizing the stability behaviour of the Dirac Hamiltonian with vectorial power potentials.